---
date: 2022-02-14 10:32
modification date: Monday 14th February 2022 10:32:39
title: rational points
aliases: [rational point]

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Last modified date: <%+ tp.file.last_modified_date() %>


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- Tags 
	- #arithmetic-geometry 
- Refs:
	- <https://www.ma.imperial.ac.uk/~anskor/IUM-IC.PDF> #resources/notes 
	- Rational points on higher dimensional varieties:
	  <https://media.ed.ac.uk/playlist/dedicated/51612401/1_c3glvibl/1_nimm7fxn> #resources/workshops 
- Links:
	- [torsor](Unsorted/torsor.md)
	- [descent](Unsorted/descent.md)
	- [Brauer group](Unsorted/Brauer%20group.md)
	- [Hasse principle](Unsorted/Hasse%20principle.md)
	- [Unsorted/sporadic point](Unsorted/sporadic%20point.md)

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# rational points

To bound $X(k)$: use [descent](Unsorted/descent.md) and [torsors](Unsorted/torsor.md), or the [Brauer-Manin obstruction](Brauer-Manin%20obstruction).
![](attachments/Pasted%20image%2020220319204535.png)

# Open Problems

- Concerning [height](Unsorted/height.md):
	- [Manin conjecture](Manin%20conjecture)
	- [Vojta's conjecture](Vojta's%20conjecture)

# Examples
![](attachments/Pasted%20image%2020220214103246.png)